steam for example have the ability to transfer installed games between systems that is logged in on the same profile. it would really help if battle.net got that. another function that would be useful is a folder transfer function. steam have that too.
I am not sure what you are asking here.
You can already download Blizzard games on any compatible device you want. Just log in to your Battlenet account on that device to access your game.
To transfer Blizzard games between computers, you can copy the game directory to a USB drive then just copy it to the other computer. Dowload the Battlenet Desktop App and log in with your Battlenet account and play. All of Blizzard’s modern games save your progress on Blizzard’s servers.
All that said - you do need to PURCHASE the games separately for each Platform you want to play on. PC, Xbox, Playstation, etc. Once linked to your battlenet account though the progress should transition seamlessly.
steam have a built in function, where installing a game on one pc, transfers the game through LAN rather than having to download it. that goes faster than having to download on each pc. then there is a function, where steam can move a game from one folder to another. battle.net should get those functions.